{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "高数下23、24、25页"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "第三节 平面及其方程\n",
    "一、曲面方程与空间曲线方程的概念\n",
    "在讨论平面与空间直线之前，先引入有关曲面方程与空间曲线方程的概念。\n",
    "\n",
    "像在平面解析几何中把平面曲线当作动点的轨迹一样，在空间解析几何中，任何曲面或曲线都看作点的几何轨迹。在这样的意义下，如果曲面 S 与三元方程 \n",
    "F(x,y,z)=0                              (3-1) \n",
    "有如下关系：\n",
    "\n",
    "（1）曲面 S 上任一点的坐标都满足方程（3-1）；\n",
    "\n",
    "（2）不在曲面 S 上的点的坐标都不满足方程（3-1），\n",
    "那么，方程（3 - 1）就叫做曲面 S 的方程，而曲面 S 就叫做方程（3 - 1）的图形（图 8 - 28）。\n",
    "\n",
    "空间曲线可以看作两个曲面 S1,S2的交线。设\n",
    "\n",
    "F(x,y,z)=0和G(x,y,z)=0\n",
    "\n",
    "分别是这两个曲面的方程，它们的交线为 C（图8-29）。因为曲线 C 上的任何点的坐标应同时满足这两个曲面的方程，所以应满足方程组\n",
    "\n",
    "$\\left\\{\\begin{array}{l}\n",
    "F(x, y, z)=0, \\\\\n",
    "G(x, y, z)=0 .                                                         \n",
    "\\end{array}\\right.$\n",
    "(3-2)\n",
    "\n",
    "\n"
   ]
  },
  {
   "attachments": {
    "图8-28.png": {
     "image/png": 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"
    },
    "图8-29.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![图8-28.png](attachment:图8-28.png)                            ![图8-29.png](attachment:图8-29.png)"
   ]
  },
  {
   "attachments": {
    "图8-30.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "反过来，如果点 M不在曲线 C上，那么它不可能同时在两个曲面上，所以它的坐标不满足方程组(3-2)。因此，曲线 C可以用方程组(3-2)来表示。方程组(3-2)就叫做空间曲线 C 的方程，而曲线 C就叫做方程组(3-2)的图形。\n",
    "\n",
    "在本节和下一节里，我们将以向量为工具，在空间直角坐标系中讨论最简单的曲面和曲线--平面和直线。\n",
    "\n",
    "二、平面的点法式方程\n",
    "\n",
    "如果一非零向量垂直于一平面，这向量就叫做该平面的法线向量。容易知道，平面上的任一向量均与该平面的法线向量垂直。\n",
    "\n",
    "因为过空间一点可以作而且只能作一平面垂直于一已知直线，所以当平面II上一点 $M_{0}(x_{0}, y_{0}, z_{0})$ 和它的一个法线向量 $n=(A,B,C)$ 为已知时，平面 II 的位置就完全确定了。下面我们来建立平面 II 的方程。\n",
    "\n",
    "设 $M(x,y,z)$ 是平面 II 上的任一点（图8-30）。\n",
    "\n",
    "则向量 $\\overrightarrow{M_{0}M}$ 必与平面 II 的法线向量 $n$ 垂直，即它们的数量积等于零：\n",
    "\n",
    "$$\n",
    "n \\cdot \\overrightarrow{M_{0}M} = 0.\n",
    "$$\n",
    "\n",
    "因为 $n=(A, B, C), \\overrightarrow{M_{0}M}=(x-x_{0}, y-y_{0}, z-z_{0})$，所以有：                              \n",
    "\n",
    "$$\n",
    "A(x-x_{0})+B(y-y_{0})+C(z-z_{0})=0.\n",
    "$$\n",
    "\n",
    "这就是平面 II 上任一点 $M$ 的坐标 $x,y,z$ 所满足的方程。                            ![图8-30.png](attachment:图8-30.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "反过来，如果 $M(x,y,z)$ 不在平面 $II$ 上，那么向量 $\\overrightarrow{M_{0}M}$ 与法线向量 $n$ 不垂直，从而 $n \\cdot \\overrightarrow{M_{0}M} \n",
    "eq 0$，即不在平面 $II$ 上的点 $M$ 的坐标 $x,y,z$ 不满足方程（3-3）。\n",
    "\n",
    "由此可知，平面 $II$ 上的任一点的坐标 $x,y,z$ 都满足方程（3-3）；不在平面 $II$ 上的点的坐标都不满足方程（3-3）。这样，方程（3-3）就是平面 $II$ 的方程，而平面 $II$ 就是方程（3-3）的图形。因为方程（3-3）是由平面 $II$ 上的一点 $M_{0}(x_{0}, y_{0}, z_{0})$ 及它的一个法线向量 $n=(A,B,C)$ 确定的，所以方程（3-3）叫做平面的点法式方程。\n",
    "\n",
    "## 例1\n",
    "求过点 $(2,-3,0)$ 且以 $n=(1, -2, 3)$ 为法线向量的平面的方程。\n",
    "\n",
    "**解** 根据平面的点法方程 (3-3), 得所求平面的方程为\n",
    "\n",
    "$$\n",
    "(x-2)-2(y+3)+3z=0,\n",
    "$$\n",
    "即\n",
    "\n",
    "$$\n",
    "x-2y+3z-8=0.\n",
    "$$\n",
    "\n",
    "## 例2\n",
    "求过三点 $M_{1}(2, -1,4)$、$M_{2}(-1,3, -2)$ 和 $M_{3}(0,2,3)$ 的平面的方程。\n",
    "\n",
    "**解** 先找出这平面的法线向量 $n$。因为向量 $n$ 与向量 $M_{1}M_{2}$ 和 $\\bar{M}_{1}M_{3}$ 都垂直，而 $M_{1}M_{2}=(-3, 4, -6), M_{1}M_{3}=(-2, 3, -1)$，所以可取它们的向量积为 $n$，即 \n",
    "$$\n",
    "n=\\bar{M_{1}M_{2}}\\times \\bar{M_{1}M_{3}}=\\left |\\begin{matrix} i&j&k\\\\ -3&4&-6\\\\ -2&3&-1\\end{matrix} \\right |=14i+9j-k,\n",
    "$$\n",
    "根据平面的点法式方程 (3-3), 得所求平面的方程为\n",
    "\n",
    "$$\n",
    "14(x-2)+9(y+1)-(z-4)=0,\n",
    "$$\n",
    "即\n",
    "\n",
    "$$\n",
    "14x+9y-z-15=0.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "平面方程为：X - 2*Y + 3*Z - 8\n",
      "点（2, -3, 0）是否满足平面方程：True\n",
      "点（2, -3, 0）是否满足另一个假设的平面方程：True\n"
     ]
    }
   ],
   "source": [
    "import sympy as sp\n",
    "\n",
    "# 定义符号变量\n",
    "X, Y, Z = sp.symbols('X Y Z')\n",
    "\n",
    "# 给定的点和向量\n",
    "point = sp.Matrix([2, -3, 0])\n",
    "normal_vector = sp.Matrix([1, -2, 3])\n",
    "\n",
    "# 计算平面方程（点法式）\n",
    "plane_equation = normal_vector.dot(sp.Matrix([X, Y, Z])) - normal_vector.dot(point)\n",
    "plane_equation_simplified = sp.simplify(plane_equation)\n",
    "\n",
    "# 打印平面方程\n",
    "print(f\"平面方程为：{plane_equation_simplified}\")\n",
    "\n",
    "# 验证点（2, -3, 0）是否满足平面方程\n",
    "point_satisfaction = plane_equation_simplified.subs({X: 2, Y: -3, Z: 0})\n",
    "print(f\"点（2, -3, 0）是否满足平面方程：{point_satisfaction == 0}\")\n",
    "\n",
    "# 验证另一个平面方程（假设与给定平面平行）\n",
    "another_plane_equation = X - 2*Y + 3*Z - 8\n",
    "point_satisfaction_another = another_plane_equation.subs({X: 2, Y: -3, Z: 0})\n",
    "print(f\"点（2, -3, 0）是否满足另一个假设的平面方程：{point_satisfaction_another == 0}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "法线向量n为：[14  9 -1]\n",
      "平面方程系数为：A=14, B=9, C=-1, D=-15\n",
      "平面方程为：14x + 9y + -1z + -15 = 0\n",
      "点M1([ 2 -1  4])是否在平面上：True\n",
      "点M2([-1  3 -2])是否在平面上：True\n",
      "点M3([0 2 3])是否在平面上：True\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# 定义三个点的坐标\n",
    "M1 = np.array([2, -1, 4])\n",
    "M2 = np.array([-1, 3, -2])\n",
    "M3 = np.array([0, 2, 3])\n",
    "\n",
    "# 计算向量MM2和MM3\n",
    "MM2 = M2 - M1\n",
    "MM3 = M3 - M1\n",
    "\n",
    "# 计算法线向量n，即MM2和MM3的向量积\n",
    "n = np.cross(MM2, MM3)\n",
    "\n",
    "# 打印法线向量n\n",
    "print(f\"法线向量n为：{n}\")\n",
    "\n",
    "# 使用点法式方程验证平面方程\n",
    "# 选择点M1(2, -1, 4)代入平面方程\n",
    "# 平面方程为：n · (P - M1) = 0，其中P是平面上的任意一点，n是法线向量\n",
    "# 展开后得到：n_x * (x - 2) + n_y * (y + 1) + n_z * (z - 4) = 0\n",
    "# 将n的坐标值代入上式，得到平面方程\n",
    "\n",
    "# 由于n可能是非单位向量，我们需要先计算n的模长，然后将其标准化（可选步骤，但有助于理解）\n",
    "norm_n = np.linalg.norm(n)\n",
    "standardized_n = n / norm_n\n",
    "\n",
    "\n",
    "# 平面方程系数\n",
    "A, B, C = n\n",
    "\n",
    "# 常数项D，通过代入点M1计算得到\n",
    "D = -np.dot(n, M1)\n",
    "\n",
    "# 打印平面方程系数和常数项\n",
    "print(f\"平面方程系数为：A={A}, B={B}, C={C}, D={D}\")\n",
    "\n",
    "# 打印平面方程\n",
    "print(f\"平面方程为：{A}x + {B}y + {C}z + {D} = 0\")\n",
    "\n",
    "# 验证点M1, M2, M3是否满足平面方程（应该满足，因为它们是用来定义平面的点）\n",
    "def verify_point_on_plane(point, A, B, C, D):\n",
    "    return np.isclose(A * point[0] + B * point[1] + C * point[2] + D, 0)\n",
    "\n",
    "print(f\"点M1({M1})是否在平面上：{verify_point_on_plane(M1, A, B, C, D)}\")\n",
    "print(f\"点M2({M2})是否在平面上：{verify_point_on_plane(M2, A, B, C, D)}\")\n",
    "print(f\"点M3({M3})是否在平面上：{verify_point_on_plane(M3, A, B, C, D)}\")"
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